find the principal unit normal vector to the curve

find the principal unit normal vector to the curve at the specific value of the parameter.

i need to use this formula

so, to find r'(t)

so, now to find the magnitude: simplified

puting them together

From here is where i get lost

I need to find T'(t)

I can seem to follow the solutions manual. I think they are using the quiotient rule due to the denominator having the 3/2

fraction. But if they are i still cant see how they are doing it.

Can anyone help me work out the next step for T'(t)?

Thank you so much!!!

Re: find the principal unit normal vector to the curve

Differentiating,

We find the magnitude,

And therefore,

Re: find the principal unit normal vector to the curve

in your second step the first arrow before Differentiating, im not sure how you got j

for i did you just bring up the denominator? doesnt make sense

Re: find the principal unit normal vector to the curve

Quote:

Originally Posted by

**icelated** in your second step the first arrow before Differentiating, im not sure how you got j

for i did you just bring up the denominator? doesnt make sense

Did you forget these properties of exponents from algebra?

Re: find the principal unit normal vector to the curve

Wow, okay how did i miss that! I wasnt splitting the i and j up. Once i did now i can see the answer fall out.